On Quantum Unique Ergodicity for Linear Maps of the Torus
The problem of “quantum ergodicity” addresses the limiting distribution of eigenfunctions of classically chaotic systems. I survey recent progress on this question in the case of quantum maps of the torus. This example leads to analogues of traditional problems in number theory, such as the classical conjecture of Gauss and Artin that any (reasonable) integer is a primitive root for infinitely many primes, and to variants of the notion of Hecke operators.
KeywordsPrimitive Root Quantum Ergodicity Primitive Root Modulo Quantum Unique Ergodicity Phase Space Average
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